Thread: Barycentric Time Dilation

Suppose this scenario, two orbiting stars with let's say equal masses to the sun. With both orbiting the common point, the barycentre, would gravitational time dilation occur at the barycetnre occur equally as if you were at a hypothetical point on either star?

If that's not clear I'm not sure how I can make that question clearer.

So theoretically would at the equivalent time dilation occur (or occur at all) at the barycentre?

Gravitational time dilation is a result of space-time curvature; since gravitational fields ( =curvature ) extend into infinity, they would be present at the barycenter as well. Hence time dilation also happens at the barycenter.

So in the same way a man would orbit the earth the centre of mass being the centre of the earth the time dilation propogates relative from there, would the same be said for the barycentre of two stars? In other words would there be technically a 'third star' at the centre of the two at which the equivalent time dilation would occur and propogate from just as it would equally from the centre of the two stars each retrospectively?

Originally Posted by Quantime

So in the same way a man would orbit the earth the centre of mass being the centre of the earth the time dilation propogates relative from there, would the same be said for the barycentre of two stars? In other words would there be technically a 'third star' at the centre of the two at which the equivalent time dilation would occur and propogate from just as it would equally from the centre of the two stars each retrospectively?

I am not entirely certain how you mean this. In any case, you can picture the barycenter of two masses as the superposition of two gravitational fields. As such there is definitely gravitational time dilation present; actually calculating this would not be so easy, if one was to base this on general relativity.

Originally Posted by Markus Hanke

Originally Posted by Quantime

So in the same way a man would orbit the earth the centre of mass being the centre of the earth the time dilation propogates relative from there, would the same be said for the barycentre of two stars? In other words would there be technically a 'third star' at the centre of the two at which the equivalent time dilation would occur and propogate from just as it would equally from the centre of the two stars each retrospectively?

I am not entirely certain how you mean this. In any case, you can picture the barycenter of two masses as the superposition of two gravitational fields. As such there is definitely gravitational time dilation present; actually calculating this would not be so easy, if one was to base this on general relativity.

Would the superposition not cancel out the curvature, i.e. would the curvature not be zero? Or would it be like a plateau below the level of zero curvature if presented in 2D, like the bottom of a bowl, with zero curvature level with the rim (if that makes sense)?

Originally Posted by KALSTER

Would the superposition not cancel out the curvature, i.e. would the curvature not be zero? Or would it be like a plateau below the level of zero curvature if presented in 2D, like the bottom of a bowl, with zero curvature level with the rim (if that makes sense)?

No, they do not cancel out, even though I cannot think of any way to visualize this in 2D. Your idea with the plateau is probably as good as it gets, even though one must be really careful with an analogue like that.

Analogues are all I have without the math ability unfortunately. Thanks.

Originally Posted by KALSTER

Would the superposition not cancel out the curvature, i.e. would the curvature not be zero? Or would it be like a plateau below the level of zero curvature if presented in 2D, like the bottom of a bowl, with zero curvature level with the rim (if that makes sense)?

Maybe the best way to look at this is the elastic sheet analogy. The two planets each cause a "dent" in the sheet. Now imagine that the two are close enough that the "dents" visibly merge at a point half way between. A little "saddle" will form, shallower than the dent made by the Planets, but still below the "normal" sheet level. Since the Planet's are of equal mass, this saddle also is at the barycenter.

Now in this analogy, the slope of the sheet at any point is the strength of the local gravity and the depth signifies difference in gravitational potential. At the barycenter you would have zero gravity, but still would have time dilation due to gravitational potential. Of course, it would only be is this situation, where the planet masses are equal, that the saddle will coincide with the barycenter. (For example, with the Earth and Moon the saddle is closer to the Moon, while the Barycenter would be under the Earth's Surface.)

I think if you work through it you will find that an observer at the barycentre would be blueshifted when viewed from the surface of either star and conversely, an observer on the surface of either star would be redshifted when viewed from the barycentre.

So I am guessing that the time-dilation would be less at the barycentre than it would be on the surface of either star.